Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at T_c= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β / υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.     

Synthesis and Biological Screening of 2‐Substituted 5,6‐Dihydro‐5‐oxo‐ 4H‐1,3,4‐oxadiazine‐4‐propanenitriles and of Their Intermediates

To evaluate the effect of substituents on biological activities of electron‐rich N‐containing heterocycles, the variably 2‐substituted 5,6‐dihydro‐5‐oxo‐4H‐1,3,4‐oxadiazine‐4‐propanenitriles 26 – 33 were synthesized and evaluated for antibacterial, antifungal, and enzyme‐inhibition activities. The target compounds were obtained from alkyl 4‐ or 3‐hydroxy benzoates 1 and 2 , respectively, and from methyl indoleacetate 3 . The phenolic OH group of benzoates 1 and 2 were substituted with p‐toluenesulfonyl (→ 4 and 5 ), benzoyl (→ 6 and 7 ), and benzyl groups (→ 8 and 9 ) and then converted to 5,6‐dihydro‐5‐oxo‐4H‐1,3,4‐oxadiazine‐4‐propanenitriles. To establish structure‐activity relationships (SAR), a pharmacological screening of the intervening intermediates was also conducted, which revealed that the intermediate hydrazide 11 possesses significant antimicrobial and MAO‐A inhibiting properties and intermediates 12, 24, 28 , and 29 appreciable antifungal activities. Compound 7 inhibits α‐chymotrypsin.     

Polymeric structure of (ethyl­ene­diamine)silver(I) 3‐nitro­benzoate monohydrate

In the ternary title compound, catena‐poly­[[silver(I)‐μ‐ethylenedi­amine‐κ²N:N′] 3‐nitro­benzoate monohydrate], {[Ag(C₂H₈N₂)](C₇H₄NO₄)·H₂O}_n, the Ag atom is bicoordinated in a linear configuration by two different N atoms from two symmetry‐related ethyl­enedi­amine ligands, thus giving linear polymeric chains with an [–Ag—N—C—C—N–]_n backbone running parallel to the a axis. In the crystal packing, these linear chains are interconnected by N—H⃛O and O—H⃛O hydrogen bonds to form layers parallel to the ab plane.     

meso‐Bis­(phenyl­sulfinyl)­methane

The title compound, meso‐C₁₃H₁₂O₂S₂, is in an anti conformation, with R and S configurations around the S atoms. The two O atoms are trans to each other, and the same applies for the two benzene rings. The phenyl­sulfinyl groups are nearly orthogonal to the central di­thio­methane group, and the orientation of the two phenyl rings are determined by the interactions in which they are involved. The packing is built from molecular columns stabilized by weak C—H⋯O interactions.     

Bis(2‐amino­pyridine‐κN1)(benzoato‐κO)silver(I)

In the title compound, [Ag(C₇H₅O₂)(C₅H₆N₂)₂], the Ag^I atom is tricoordinated by two independent pyridine N atoms and one benzoate O atom in a nearly planar geometry. An intramolecular N—H⃛O hydrogen bond forms an S(8) graph ring. The packing is built from molecular layers stabilized by two types of N—H⃛O hydrogen bond. Intermolecular Ag⃛N and intramolecular Ag⃛O contacts were also observed, together with three weak intermolecular C—H⃛π interactions.     

N‐{4‐Bromo‐2‐[(3‐bromo‐1‐phenylsulfonyl‐1H‐indol‐2‐yl)methyl]‐5‐methoxyphenyl}acetamide

In the title compound, C₂₄H₂₀Br₂N₂O₄S, the indole ring system is planar and the S atom has a distorted tetrahedral configuration. The sulfonyl‐bound phenyl ring is orthogonal to the indole ring system and the conformation of the phenyl­sulfonyl substituent with respect to the indole moiety is influenced by intramolecular C—H⃛O hydrogen bonds involving the two sulfonyl O atoms. The mean plane through the acetyl­amido group makes a dihedral angle of 57.0 (1)° with the phenyl ring of the benzyl moiety. In the crystal, glide‐related mol­ecules are linked together by N—H⃛O hydrogen bonds and C—H⃛π interactions to form molecular chains, which extend through the crystal. Inversion‐related chains are interlinked by C—H⃛π interactions to form molecular layers parallel to the bc plane. These layers are interconnected through π–π interactions involving the five‐ and six‐membered rings of the indole moiety.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

Dust ion‐acoustic solitons with trapped q‐non‐extensive electrons,dissipative processes,and streaming ions

The characteristics of dust ion‐acoustic waves (DIAWs) that are excited because of streaming ions and hot q‐non‐extensive electrons obeying a vortex‐like distribution are investigated. By exploiting a pseudo‐potential technique, we have derived an energy integral equation. The presence of non‐extensive q‐distributed hot trapped electrons and a streaming ion beam has been shown to influence soliton structure quite significantly. The evolution of the soliton‐like perturbations in complex plasmas, taking into account the dissipation processes, are also investigated, obtained by numerically solving the modified Schamel, equation whose widths are dependant on electron trapping efficiency β. Our illustrations indicate that compressive DIAWs develop in this plasma. As the plasmas in reality have a relative flow, such an analysis can be used to understand the DIA solitary structures observed in the mesospheric noctilucent clouds.     

Dissipative ion acoustic solitary waves in collisional,magneto‐rotating,non‐thermal electron–positron–ion plasma

The linear and non‐linear dynamics of ion acoustic waves are investigated in three‐component magnetized plasma consisting of cold inertial ions and non‐thermal electrons and positrons. The non‐thermal components are modelled by the hybrid distribution, representing the combination of two (kappa and Cairn's) non‐thermal distributions. The relevant processes, including the slow rotation of plasma along the magnetic field axis and collision between ions and neutrals, are taken into consideration. It is shown that the non‐linear dynamics of the considered system are governed by the Zakharov–Kuznetsov equation in modified form. In the general dissipation regime, the effects of the two non‐thermal distributions on the solitary waves are compared. The effects of other plasma parameters, such as collisional and rotational frequency, are also discussed in detail.     

Dispersion properties of electron acoustic waves in degenerate and non‐degenerate quantum plasmas

The longitudinal response functions are used to generalize the dispersion properties of electron acoustic waves (EAWs) in the presence of quantum recoil, for isotropic, non‐relativistic, degenerate/non‐degenerate plasmas. In order to study the EAWs, the constituents of non‐degenerate (thermal) plasma are considered to be of two groups of electrons having different number density and temperature, namely the cold electrons and the hot electrons. Similarly in degenerate (Fermi) plasma the two population of electrons are considered to be the thinly populated and the thickly populated electrons. The sparsely populated electrons are termed as cold electrons while the densely populated ones are termed as hot electrons. The ions are stationary which form the neutralizing background. The absorption coefficients for Landau damping with the inclusion of the quantum recoil in both plasmas are calculated and discussed. The results are discussed in the context of laser‐produced plasma.